Classroom Voting Questions Multivariable Calculus

							             Classroom Voting Questions:
                Multivariable Calculus

  15.2 Optimization

1. Estimate the global maximum and minimum of the functions whose level curves are
   given below. How many times does each occur?




   (a) Max ≈ 6, occurring once; min ≈ −6, occurring once
   (b) Max ≈ 6, occurring once; min ≈ −6, occurring twice
   (c) Max ≈ 6, occurring twice; min ≈ −6, occurring twice
   (d) Max ≈ 6, occurring three times; min ≈ −6, occurring three times
   (e) None of the above


2. What are the global maximum and minimum values of f (x, y) = x2 + y 2 on the
   triangular region in the first quadrant bounded by x + y = 2, x = 0, y = 0?

   (a) Maximum = 2, Minimum = -2
   (b) Maximum = 2, Minimum = 0


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    (c) Maximum = 4, Minimum = 2
   (d) Maximum = 4, Minimum = 0


3. The function f (x, y) = x3 + 12xy + y 4 has:

   (a) no global maxes or mins
   (b) a global max, but no global min
    (c) a global min, but no global max
   (d) both a global min and a global max


4. Which of the following would be enough evidence to conclude that a smooth function
   f (x, y) has a global min?

   (a) D is always positive
   (b) fxx > 0 and fyy > 0
    (c) f (x, y) has no saddle points or local maxes
   (d) none of the above




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